Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces
Rabian Wangkeeree, Pakkapon Preechasilp · Journal of Inequalities and Applications · 2013
The purpose of this paper is to study the strong convergence theorems of Moudafi’s viscosity approximation methods for a nonexpansive mapping T in CAT(0) spaces without the property . For a contraction f on C and , let be the unique fixed point of the contraction ; i.e., and where is arbitrarily chosen and satisfies certain conditions. We prove that the iterative schemes and converge strongly to the same point such that , which is the unique solution of the variational inequality (VIP) By using the concept of quasilinearization, we remark that the proof is different from that of Shi and Chen in J. Appl. Math. 2012:421050, 2012. In fact, strong convergence theorems for two given iterative schemes are established in CAT(0) spaces without the property .